मराठी

Find the Distance Between the Points (I) A(9,3) and B(15,11)

Advertisements
Advertisements

प्रश्न

Find the distance between the points

(i) A(9,3) and B(15,11)

 

Advertisements

उत्तर

A(9,3) and B(15,11)
The given points are A(9,3) and B(15,11)
`Then ( x_2= 9,y_1=3) and (x_2 = 15 , y_2=11)`

`AB=sqrt((x_2-x_1)^2 +(y_2-y_1)^2)`

`=sqrt((15-9)^2 +(11-3)^2)`

`=sqrt((6)^2+(8)^2)`

`=sqrt(36+64)`

`= sqrt(100)`

= 100 units

 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Coordinate Geometry - Exercises 1

APPEARS IN

आर. एस. अग्रवाल Mathematics [English] Class 10
पाठ 6 Coordinate Geometry
Exercises 1 | Q 1.1

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.


Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.


Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.


Find the distance of the following points from the origin:

(i) A(5,- 12)


Find the distance between the following pair of point.

T(–3, 6), R(9, –10)


Find the distances between the following point.

P(–6, –3), Q(–1, 9) 


Find the distance between the following point :

(p+q,p-q) and (p-q, p-q) 

Find the distance between the following point :

(Sin θ - cosec θ , cos θ - cot θ) and (cos θ - cosec θ , -sin θ - cot θ)


The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.


Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.


PQR  is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.


The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.


If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.


Show that P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.


Show that the point (0, 9) is equidistant from the points (–4, 1) and (4, 1).


The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.


The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.


Case Study

Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites.
A guard, stationed at the top of a 240 m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer is an instrument used for measuring angles or slopes(tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be 30°.

  1. Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
  2. After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

What is the distance of the point (– 5, 4) from the origin?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×